Question

The table shows the salary of an employee after x years of working for Company A. The linear function y = 200x + $29,000 represents the salary, y, of an employee in the same position working at Company B for x number of years. Which statement BEST compares the rate of change per year for the employee at Company A and the employee at Company B?

A) The rate of change per year for Company A's employee is $50 less than Company B's rate of change per year.

B) The rate of change per year for Company A's employee is $150 greater than Company B's rate of change per year.

C) The rate of change per year for Company B's employee is $200 greater than Company A's rate of change per year.

D) The rate of change per year is the same for Company A and Company B.

Answer 1

The Answer is A

Explanation:

The slope of each function is the rate of change. Company A's rate of change:

`($33,750-$33,450)/(2)` = $150. Company B's rate of change per year: y =

$200x + $29,000 → the slope is 200.

$200 − $150 = $50 greater per year

Answer 2

Option A The rate of change per year for Company A's employee is $50 less than Company B's rate of change per year.

Explanation:

step 1

Find out the rate of change per year for the employee at Company A

we have

(1,33,300) and (6,34,050)

Find the slope of the linear function

`m=(34,050-33,300)/(6-1)=150`

The rate of change is equal to the slope

therefore

The rate of change per year for the employee at Company A is $150

step 2

Find out the rate of change per year for the employee at Company B

we have

`y=200x+29,000`

This is the equation of the line into slope intercept form

so

the slope
`m=200`

therefore

The rate of change per year for the employee at Company B is $200

step 3

Compare the rate of change

Company A is $150 per year

Company B is $200 per year

therefore

The rate of change per year for Company A's employee is $50 less than Company B's rate of change per year.